METALLURGY

& S3 MECHANICAL
S3 MECHANICAL
MATERIALS SCIENCE
MET 205

Dr. Roja Abraham Raju

Associate Professor
Mar Baselios Christian
College of Engineering and Technology, Peermde- 685531
Email: rojaabrahamraju@mbcpeermde.com
 REFERENCES

Few major references are included here. Other references may be found in individual chapters.
 Materials Science and Engineering, V. Raghavan,
Fifth Edition, Prentice Hall of India Pvt. Ltd., New Delhi, 2004.
 Material Science for Engineers, Anderson J.C. et.al., Chapman and Hall,1990
ONLINE
http://home.iitk.ac.in/~anandh/E-book.htm
As a Mechanical Engineering student have ever thought of possible reason for this?
 Why is glass brittle, while copper is ductile? What is meant by a ductile material?
 If we take two rods, one of Al and one of steel, why is it easier to bend the Al rod as
compared to the steel rod?
 How can I change properties like hardness, without changing the composition (say of 0.8% C
steel)?

 Why is wire of copper conducting, while piece of brick or wood non-conducting?

 Why is glass transparent, while any typical metal is opaque?
 Why does the electrical conductivity of Cu decrease on heating, while that of Si increases?
 Why does Iron corrode easily, while Aluminium does not (or does not seem to?!)?
 How come I can hold a molten materiazl in the liquid state below the melting point (e.g.
water can be held at sub-zero (C) temperatures), for at least some time (in many cases this is not difficult)?
 How come bubbles tend to form in a aerated drink glass around the straw and glass walls?
 What is the melting point? Is it different from the freezing point?

 Usually, good thermal conductors are also good electrical conductors. Why is this so?
Why is diamond a good thermal conductor, but not a good electrical conductor?
 If I pull a spring and then release the load, it ‘comes back’ to its original shape. However, a if
I bend an aluminium rod, does not come back to its original shape. How can one understand
these observations?
What will you learn in this course?
 Understand the basic chemical bonds, crystal structures (BCC, FCC, and
HCP), and their relationship with the properties.
 Analyze the microstructure of metallic materials using phase diagrams and
modify the microstructure and properties using different heat treatments.
 How to quantify mechanical integrity and failure in materials?
 Apply the basic principles of ferrous and non-ferrous metallurgy for
selecting materials.
 Define and differentiate engineering materials on the basis of structure and
properties for engineering applications.
Introduction

Material -> something tangible that goes into the makeup of a physical
object.

Material Science -> involves investigating the relationships that exist

between the structures and properties of materials

Material Engineering -> is, on the basis of these structure–property

correlations, designing or engineering the structure of a material to
produce a predetermined set of properties

Metallurgy -> is a domain of materials science and engineering that

studies the physical and chemical behavior of metallic elements, their
inter-metallic compounds, and their mixtures, which are called alloys.
Metallurgy encompasses both the science and the technology of metals.
 Common materials: with various ‘viewpoints’

Ceramics Glass: amorphous Graphite

Crystal Metals Polymers

1. Metals 2. Ceramics 3. Polymers 4. Composites

- aluminum - clay - polyvinyl chloride - wood
- copper - silica glass (PVC) - carbon fiber
- steel (iron alloy) - alumina - Teflon resins
- nickel - quartz - various plastics - concrete
- titanium - glue (adhesives)
- Kevlar
Material Science

• Material Science -> involves investigating the relationships that exist

between the structures and properties of materials

• Structure -> The arrangement of internal components of matter in a

material
• Properties -> Response of the material when exposed to an external
stimulus
Level of Structure

• Macrostructure -> What is visible to the naked eye

• Mircostructure -> Structure as obtained under the optical microscope
• Substructure -> Structure as obtained under an electron microscope
• Crystal structure ->Provides details upto atomic level, its arrangement
• Electronic structure -> Refers to arrangement of electrons in the outer
orbital.
• Nuclear structure -> Details regarding the constituents within the
nucleus of atoms in the material.
Properties of Engineering Materials

• Physical Properties -> Dimension, Density, Porosity

• Mechanical Properties -> Strength, hardness, toughness
• Thermal Properties -> Specific heat, conductivity
• Electrical Properties -> Resistivity, conductivity, dielectric strength
• Magnetic Properties -> Hysteresis, Permeability
• Optical Properties -> Reflection, Refraction, absorption
• Chemical Properties -> Acidity, alkalinity, oxidation, corrosion
Atomic Structure

• In order to understand the structure of materials and its correlation

to property, we have to start form the basic element of matter –The
Atom
• Atomic number
• Atomic mass
Bohr Thoery

• Electrons revolve around a positively charged nucleus in discrete orbits

(K, L, M or n=1, 2, 3 respectively) with specific levels of energy.
• Electrons positions are fixed as such, however, an electron can jump to
higher or lower energy level by absorption or emission of energy
respectively as shown in Fig. (b)
Quantum numbers

• Four parameters or numbers called Quantum numbers are needed to

describe the distribution and position of electrons in an atom. The
first three of them (n, l, ml) describe the size, shape, and spatial
orientation of the probability density distribution of electron
Electron Configuration

•  Electron configuration based on quantum numbers. Total number of

electrons in a shell is or
Valence electrons
• The electrons in the outer most shell are known as valence electrons
{Na has one valence electron (the 3s electron)}
• These electrons are responsible for chemical reaction and atomic
bonding
Stable configuration
• Look at the electron configuration of inert gases (He, Ne, Ar, Kr, Xe) in
the previous table. Their valence electron cell is completely filled
unlike any other element.
• This is known as stable configuration. Since it is the lowest energy
configuration, the valence electrons do not take part in any chemical
reaction and hence, the inertness.
Stable Configuration

• It is the tendency of every element to attain the lowest energy stable

configuration that forms the basis of chemical reactions and atomic
bonding
• Electron affinity: The electron affinity of an atom or molecule is
defined as the amount of energy released when an electron is
attached to a neutral atom or molecule in the gaseous state to form a
negative ion.
• Electronegativity, is a concept that describes the tendency of an
atom to attract a shared pair of electrons 
• Ionization energy a measure of the difficulty in removing an
electron from an atom or ion or the tendency of an atom
(lower the IE, the higher the ability to allow electrons to flow)
Atomic interaction

• When two neutral atoms are brought close to each other, they
experience attractive and repulsive force
• Attractive force is due to electrostatic attraction between electrons of
one atom and the nucleus of the other.
• Repulsive force arises due to repulsion between electrons and nuclei
of the atoms.
• The net force, FN(Fig. a), acting on the atoms is the summation of
attractive and repulsive forces.
• The distance, at which the attraction and repulsion forces are equal
r
and the net force is zero, is the equilibrium interatomic distance, o.
The atoms have lowest energy at this position.

r
• Attraction is predominant above o and repulsion is dominant below

ro (see Fig. a).

 Atomic interaction

 • The interaction energy between the pair of atoms is given by the Lennard-
Jones potential
• is the distance at which the interaction energy is zero. is the depth of the
potential well (see Fig. b) and is a measure of the bonding energy between
two atoms.
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic interaction
Atomic Bonding
• The mechanisms of bonding between the atoms are based on
electrostatic interatomic interaction.
• The types of bond and bond strength are determined by the
electronic structures of the atoms involved.
• The valence electrons take part in bonding. The atoms involved
acquire, loose or share valence electrons to achieve the lowest
energy or stable configuration of noble gases.
• Atomic bonding can be broadly classified as
i)Primary Bonding
ii)Secondary Bonding
Periodic Table
Primary Bonds
• Three types primary bonds are found in solids
1. Ionic
2. Covalent
3. Metallic

• Majority of the engineering materials consist of one of these bonds.

Many properties of the materials depend on the specific kind of bond
and the bond energy.
Ionic Bond
• Ionic bonds are generally found in compounds composed of metal
and non-metal and arise out of electrostatic attraction between
oppositely charged atoms (ions)
Covalent Bond
• In this type of bonding, atoms share their valence electrons to get a
stable configuration.
• Covalent bonds are formed between atoms of similar
electronegativity.
• C atoms in diamond are covalently bonded to each other.
• Si also has valency of four and forms SiC through covalent bonding
with C atoms.
Metallic Bond
• In metals the valence electrons are not really bound to one particular
atom, instead they form a sea or cloud of valence electrons which are
shared by all the atoms. The remaining electrons and the nuclei form what
is called the ion core which is positively charged. The metallic bond arises
out of the columbic attraction between these two oppositely charged
species –the electron cloud and the ion cores
Difference Between Primary Bonds

Ionic Bond Covalent Bond Metallic Bond

• Electrostatic force of • Electrostatic force of • Electrostatic force of
attraction between +ve and attraction between atoms by attraction between atoms by
–ve ions. sharing pair of electrons. sharing of electrons to
• Non directional as each • Directional, electrostatic electron cloud
+ion attract all neighbouring force of attraction is more • Non directional ion cores
–ve ions localised. and electron clouds take
• Bad conductor electricity • Bad conductor electricity part in bonding
• Very low thermal • Very • Good conductor electricity
low thermal
conductivity conductivity • Good thermal conductivity
• Crystalline • Non-crystalline • Crystalline
• High Melting Points • Low Melting Points • Low Melting Points
• Not Malleable • Not Malleable • Malleable
• Soluble in water • Soluble in organic solvents • Not soluble in both
Secondary Bonds
Van der Waals bonding
• Van der Waals bonding between molecules or atoms arise due to
weak attraction forces between dipoles
• The natural oscillation of atoms leading to momentary break down of
charge symmetry can generate temporary dipoles
• Dipoles can induce dipoles and attraction between opposites ends of
the dipoles leads to weak bonding
Secondary Bonds
Hydrogen Bond
• Hydrogen bond is a type of secondary bond found in molecules
containing hydrogen as a constituent.
• The bond originates from electrostatic interaction between hydrogen
and another atom of high electronegativity such as fluorine or
oxygen.
• Water molecules, for example, are connected by hydrogen bonds
Properties Based on Atomic Bonding
Generalizations regarding properties of materials

• Atomic Radius- A positive ion has a smaller radius and a negative ion have a
larger radius
• Density- Density is controlled by atomic weight. Atomic radius and
coordination number
• Melting and boiling point- Materials with deeper energy well bonds have
higher melting and boiling temperature compared to shallow energy well
bonds
• Thermal expansion- Materials with shallow energy well bonds have higher
Thermal expansion compared to deeper energy well bonds
• Strength: Materials with deeper energy well bonds
• Modulus of Elasticity: Modulus of Elasticity related to slope of net force curve
• Thermal and Electrical Conductivity : It depends on free electrons
Crystallography
Crystal
• A crystal or crystalline solid is a solid material whose
constituents (such as atoms, molecules, or ions) are arranged
in a highly ordered microscopic structure, forming a crystal
lattice that extends in all directions.
Space lattice
• A space lattice is defined as an infinite array of points in three
dimensions in which every point has surroundings identical to that of
every other point in the array.
Unit Cell

• Unit cell is smallest repeatable entity that can be used to completely

represent a crystal structure.
• Unit cell is the building block of the crystal structure and defines the
crystal structure by virtue of its geometry and the atom positions
within it.
Bravais Lattices
Space Lattices and Crystal Structure

• A space lattice combined with a basis generates a crystal structure

Space Lattice + Basis = Crystal Structure
• Basis is simple – consisting of one atom per lattice point
BCC space lattice + 1 Cr atom per lattice point = BCC crystal of Cr
FCC space lattice + 1 Cu atom per lattice point = FCC crystal of Cu
 Common crystal structures and their
properties
Coordination number is the number of nearest neighbors of an atom in a unit cell
Coordination Number - SC

1 2
4 3

5 6
8 7 Coordination number 6

•  Ne is the effective no of atoms = 8

corner atom x = 1
Coordination Number - BCC

•  Ne is the effective no of atoms = 8 corner atom x+ 1 centre atom = 2

Coordination Number - FCC
FCC Coordination Number and Effective no
of atoms

•  Ne is the effective no of atoms = 8 corner atom x+ 6

face centres x ½ = 4
Coordination Number - HCP
Atomic packing factor

• Indicates how closely atoms are packed in a unit cell and is given by
the ratio of volume of atoms in the unit cell and volume of the unit
cell

( X Ne is the effective no of atoms)

FCC lattice
•  Considering the atoms as hard spheres of radius
R
• Total volume of atoms = Ne x
• Ne is the effective no of atoms = 8 corner atom
x+ 6 face centres x ½ = 4
• The relation between R and the FCC cell side a
as shown in the figure below is a = 4 R
BCC Lattice
•  Considering the atoms as hard spheres of radius R
• Total volume of atoms = Ne x
• Ne is the effective no of atoms = 8 corner atom x+ 1 centre atom = 2
• The relation between R and a is a = 4 R
HCP Structure
• In the Hexagonal unit cell, number of atoms = 12 corner atoms x 1/6
(shared by six unit cells) + Two face atoms x 1/2 + 3 interior = 6
2R=a
• Unit cell volume = (6 x ½ x a x h) x c = (3 x a x a sin60 ⁰) x c
• The face-centered atom and the three mid-layer atoms form a
tetrahedron MNOP which has sides equal to a (as atoms at vertices touch
each other) and height of c/2. Using this tetrahedron it can be shown that
for an ideal hexagonal crystal c/a ratio = 1.633
Crystal Systems
Problems

• Copper has FCC crystal structure. Determine its density if the atomic
weight is 63.54 and atomic radius is 1.278 Ǻ
• Calculate the number of atoms per unit cell of the metal having a
lattice parameter of 2.88Ǻ and a density of 7.87 gm/cm3. Atomic
weight A= 55.85
• A metal having cubic structure has a density of 2.6 g/m, atomic
weight of 87.62 g/mol and a lattice parameter of 6.0849 Ǻ. One atom
is associated with each lattice point. Determine the crystal structure
of the metal.
• Crystalline – periodic arrangement of atoms: definite
repetitive pattern.
• Non-crystalline or Amorphous – random arrangement
of atoms.
• Crystalline solids are long range order
• Non crystalline are short range order
• Crystalline solids have a sharp melting point
• Non crystalline materials do not have a sharp melting point
• Crystalline solids are Cu, Al etc
• Non crystalline solids are fiber glass, toflon etc
Polymorphism and Allotropy
• Allotropic form of carbon are Diamond, Graphite, CNTs

• Polymorphism
As temperature increases crystal structure changes

1. Iron
a. α- Iron- ferrite - BCC
b. 912⁰C – γ Iron – Austenite - FCC
c. 1394⁰C - β iron- BCC
Titanium

• Pure titanium is polymorphic – it exists in more

crystallographic structures (phases)
• Similarly to iron
• Above 882°C the titanium is body-centered cubic material
(bcc) – b – phase
• Upon cooling below 882°C – (so-called b-transus
temperature) – b – phase martensitically transforms to
hexagonal close-packed structure - a – phase
 Miller Indices
• Conventions to specify direction and planes in a crystal
• For example: cast iron is more stronger in compression than in
tension.
• It is necessary to characterize the crystal to identify specific directions
and planes.
• Specific methods are employed to define crystal directions and
crystal planes
• Miller indices are used to specify directions and planes.
• These directions and planes could be in lattices or in crystals.
• The number of indices will match with the dimension of the lattice or
the crystal.
• E.g. in 1D there will be 1 index and 2D there will be two indices etc.
• (h,k,l) represents a point – note the exclusive use of commas
• Negative numbers/directions are denoted with a bar on top of the
number
1. [hkl] represents a direction
2. <hkl> represents a family of directions
3. (hkl) represents a plane
4. {hkl} represents a family of planes
Miller Indices for Direction:

• A vector r passing from the origin to a lattice point can be written as:

r = r1 a + r2 b + r3 c
where,
• a, b, c → basic vectors and miller indices → (r1r2r3)
• Fractions in (r1r2r3) are eliminated by multiplying all components by
their common denominator.
• [e.g. (1, ¾ ,½ ) will be expressed as (432)]
 Further points
 General Miller indices for a direction in 3D is written as [u v w].
 The length of the vector represented by the Miller indices is:

Important directions in 3D represented by Miller Indices (cubic lattice)

Z  Three important set of directions related
[011]
to the cube are:
[001] (i) cell edge ([001] type),
(ii) face diagonal ([011] type),
(iii) body diagonal ([111] type).
Memorize
these
[101] Body diagonal

[010]
Y [111]
[100] Face diagonal

[110]

Procedure as before
• (Coordinates of the final point  coordinates of the initial point).
• Reduce to smallest integer values.
Miller Indices for Planes:

Procedure
1. Identify the plane intercepts on the x, y and z-axes.
2. Specify intercepts in fractional coordinates.
3. Take the reciprocals of the fractional intercepts
• Consider the plane in pink, which is one of an infinite number of
parallel plane each a consistent distance (“a”) away from the origin
(purple planes)
• The plane intersects the x-axis at point a. It runs parallel along y and z
axes.
• Thus, this plane can be designated as (1,∞,∞)
• Likewise, the yellow plane can be designated as (∞,1,∞)
• And the green plane can be written as (∞,∞,1)
• Miller Indices are the reciprocals of the parameters of each crystal
face.
Thus:
• Pink Face = (1/1, 1/∞, 1/∞) = (100)
• Green Face = (1/∞, 1/∞, 1/1) = (001)
• Yellow Face = (1/∞, 1/1, 1/∞) = (010)
• What’s the Miller Index of this plane?
• The plane of interest cuts two of the crystallographic axes.
• Intercepts: (1,1, ∞) = (110)
• Miller Index?
• This plane cuts all three crystallographic axes.
• Intercepts = (1,1,1) = (111)
• Miller Index?
• This plane cuts two of the reference axes, but not equidimensional.
• Intercepts: (½, 1, 0) = (210)
Methodology to define crystallographic planes in cubic crystal
1. Determine the intercepts of the plane along the crystallographic
axes, in terms of unit cell dimensions. If plane is passing through
origin, there is a need to construct a plane parallel to original
plane.
2. Take the reciprocals of these intercept numbers.
3. Clear fractions.
4. reduce to set of smallest integers.
5. The three indices are enclosed in parenthesis, (hkl).
6. A family of planes is represented by {hkl}.
Importance of Miller indices

• In Materials Science it is important to have a notation system for

atomic planes since these planes influence
• Optical properties
• Reactivity
• Surface tension
• Dislocations
Some useful conventions of Miller notation:
1. If a plane is parallel to an axis, its intercept is at infinity and its Miller
index will be zero.
2. If a plane has negative intercept, the negative number is denoted by a
bar above the number. Never alter negative numbers. For example, do
not divide
3. 1, -1, -1 by -1 to get 1,1,1. This implies symmetry that the crystal may
not have!
4. The crystal directions of a family are not necessarily parallel to each
other. Similarly, not all planes of a family are parallel to each other.
5. By changing signs of all indices of a direction, we obtain opposite
direction. Similarly, by changing all signs of a plane, a plane at same
distance in other side of the origin can be obtained.
6. Multiplying or dividing a Miller index by constant has no effect on the
orientation of the plane.
7. The smaller the Miller index, more nearly parallel the plane to that axis,
and vice versa.
8. When the integers used in the Miller indices contain more than one
digit, the indices must be separated by commas. E.g.: (3,10,13)
9. By changing the signs of all the indices of (a) a direction, we obtain
opposite direction, and (b) a plane, we obtain a plane located at the
same distance on the other side of the origin.
Family of directions

Index Members in family for cubic lattices Number

<100> [100],[100],[010],[0 10],[001],[00 1] 3x2=6

[110],[110],[1 10],[1 10],[101],[101],[10 1],[10 1],[011],[0 11],[01 1],[0 1 1] 6x2=

<110>
12

<111> [111],[111],[1 11],[11 1],[1 11],[11 1],[1 1 1],[1 1 1] 4x2=8

Deformation of Metals
• When subjected to an external force or load, the material suffers a
change of shape- Deformation
• Temporary Deformation – Elastic
• Permanent Deformation – Plastic
• Deformation is due to adjustments or displacement in atomic
arrangement within the crystal
• Load applied – tensile, compressive or shear
Elastic Deformation

• A solid subjected to an applied force, the atoms are displaced from

their normal position, just enough to develop an attractive force
between atom to balance the applied load.
Plastic Deformation
Plastic Deformation by Slip

• Slip is the prominent mechanism of plastic deformation in metals. It

involves sliding of blocks of crystal over one other along definite
crystallographic planes, called slip planes.
• It is analogous to a deck of cards when it is pushed from one end. Slip
occurs when shear stress applied exceeds a critical value.
• During slip each atom usually moves same integral number of atomic
distances along the slip plane producing a step, but the orientation of
the crystal remains the same.
• Slip plane is the plane of greatest atomic density, and the slip
direction is the close packed direction within the slip plane.
• The Plane on which slip occurs is called slip plane
• The direction along which atoms move is the slip direction
• Even if the material is subjected to tensile or compressive load, it is the
shear component which causes the plastic deformation
• Slip occurs readily along certain crystallographic planes and directions
with in a crystal.
• A set of such favorable planes and directions are called slip system
Crystal Structure Slip Plane Slip Directon

FCC {111} <110>

BCC {110} <111>
HCP {0001} <11ƻ0>
Schmid’s Law

• Consider a single crystal of metal of cylindrical

Shape
• A tensile force F is applied
• Angle between slip direction and applied force
Is λ
• Ψ is inclination of normal to slip plane
• Sum of λ and Ψ need not be 90⁰
•  A shear for acting along slip direction to obtain a slip, by the applied
load
= F cos λ
• If area of cross section of cylindrical bar is
A= /cos ψ
Shear stress along the slip direction can be
= = cos λ cos ψ
• Since =, normal stress applied to the bar
= cos λ cos ψ
• Equation is known as schmid’s law
• Critical Shear Stress/ Critical Resloved Shear Stress
Plastic Deformation by Twining
• Portion of crystal takes up an orientation that is related to the
orientation of the rest of the untwined lattice in a definite,
symmetrical way.
• The twinned portion of the crystal is a mirror image of the parent
crystal.
• The plane of symmetry is called twinning plane.
• The important role of twinning in plastic deformation is that it causes
changes in plane orientation so that further slip can occur.
 Distinguish Between Slip and Twining

Slip Twining
• Sliding movement of atom on slip • Displacive movement of atom relative
planes to each other
• Orientation of crystal above and • Orientation on either side of twinning
below slip plane is same plane are different ( Mirror Image)
• Atomic movement are of one or more • Atomic Movement are a fraction of
atomic spacing atomic spacing
• Initiates at lower stress values • At higher stress values
• Observed in all type of crystals • More significant in HCP Crystals
• Seen as line under microscope • Seen as band under microscope
Brittleness of BCC and HCP and Ductility of
FCC
• FCC crystal have maximum atomic density there at {111} plane and
<110> direction
• These slip systems are well distributed in space so there is always one
favorable slip system for plastic deformation

Crystal Structure Slip Plane Slip Directon

FCC {111} <110>
BCC {110} <111>
HCP {0001} <11ƻ0>